Provided by: liblapack-doc_3.3.1-1_all #### NAME

```       LAPACK-3  -  computes a split Cholesky factorization of a real symmetric positive definite
band matrix A

```

#### SYNOPSIS

```       SUBROUTINE SPBSTF( UPLO, N, KD, AB, LDAB, INFO )

CHARACTER      UPLO

INTEGER        INFO, KD, LDAB, N

REAL           AB( LDAB, * )

```

#### PURPOSE

```       SPBSTF computes a split Cholesky factorization of a real symmetric positive definite  band
matrix A.
This routine is designed to be used in conjunction with SSBGST.
The factorization has the form  A = S**T*S  where S is a band matrix
of the same bandwidth as A and the following structure:
S = ( U    )
( M  L )
where U is upper triangular of order m = (n+kd)/2, and L is lower
triangular of order n-m.

```

#### ARGUMENTS

```        UPLO    (input) CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

N       (input) INTEGER
The order of the matrix A.  N >= 0.

KD      (input) INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

AB      (input/output) REAL array, dimension (LDAB,N)
On entry, the upper or lower triangle of the symmetric band
matrix A, stored in the first kd+1 rows of the array.  The
j-th column of A is stored in the j-th column of the array AB
as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
On exit, if INFO = 0, the factor S from the split Cholesky
factorization A = S**T*S. See Further Details.
LDAB    (input) INTEGER
The leading dimension of the array AB.  LDAB >= KD+1.

INFO    (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the factorization could not be completed,
because the updated element a(i,i) was negative; the
matrix A is not positive definite.

```

#### FURTHERDETAILS

```        The band storage scheme is illustrated by the following example, when
N = 7, KD = 2:
S = ( s11  s12  s13                     )
(      s22  s23  s24                )
(           s33  s34                )
(                s44                )
(           s53  s54  s55           )
(                s64  s65  s66      )
(                     s75  s76  s77 )
If UPLO = 'U', the array AB holds:
on entry:                          on exit:
*    *   a13  a24  a35  a46  a57   *    *   s13  s24  s53  s64  s75
*   a12  a23  a34  a45  a56  a67   *   s12  s23  s34  s54  s65  s76
a11  a22  a33  a44  a55  a66  a77  s11  s22  s33  s44  s55  s66  s77
If UPLO = 'L', the array AB holds:
on entry:                          on exit:
a11  a22  a33  a44  a55  a66  a77  s11  s22  s33  s44  s55  s66  s77
a21  a32  a43  a54  a65  a76   *   s12  s23  s34  s54  s65  s76   *
a31  a42  a53  a64  a64   *    *   s13  s24  s53  s64  s75   *    *
Array elements marked * are not used by the routine.

LAPACK routine (version 3.2)               April 2011                            SPBSTF(3lapack)
```